a. Do some research and find a city that has experienced population growth.
Determine its population on January 1st of a certain year. Write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of exponential growth. Describe
the variables and numbers that you used in your equation.
b. Find another city whose population starts larger than the city in part (a), but
that during this same time experienced population decline. Determine its
population for January 1st of the same year you picked for part (a). Write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of population decline. Describe
the variables and numbers that you used in your equation.
c. Explain the similarities and differences between your equations in (a) and
(b).
d. During what year will the population of city (a) first exceed that of city (b)?
Show all of your work and explain your steps.
e. During what year will the population of city (a) be at least twice the size of
the population of city (b)? Show all of your work and explain your
steps.
9 answers
Anyway, here's my work for Task 1 of this portfolio:
Suppose you start with one single bacterium. Make a table of values showing the number of bacteria that will be present after each hour for the first six hours using the hourly growth rate that you selected. Then determine how many bacteria will be present once 24 hours have passed.
I chose the number 3.
Number of Hours Number of Bacteria
0 1
1 3
2 9
3 27
4 81
5 243
6 729
After 24 hours, there will be 282,429,536,481 bacteria
Explain why this table represents exponential growth.
This table represents exponential growth because the number of bacteria is always multiplied by 3.
Using this example, explain why any nonzero number raised to a power of zero is equal to one.
The reason any nonzero number raised to power of zero equals one is that any number to the zero power is the product of no numbers, which is multiplicative identity 1.
Write a rule for this table.
y=1×3^x
Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.
I would change the rule into y=100×3^x.
My first rule started from 1 bacterium, and would multiply by 3 for x times. Now that I am starting with 100 bacteria but still using the same growth factor (3x), I would change 1 from my earlier rule into 100, but keep the remaining values same.
I send my work in separate docs. I got 100% in this one, my teacher is waiting for the rest of the documents. I do not think the same system goes for you, but me and my teacher, Mrs. Claire (I'm pretty sure you have the same teacher!) had a "pact" on this. If I get good feedback on this, I will definitely get back. If I do not, you can tell that I did not get a grade 97%+. So, sorry in advance if that happens!
3 answers